scholarly journals On the Number of Vedernikov–Ein Irreducible Components of the Moduli Space of Stable Rank 2 Bundles on the Projective Space

2018 ◽  
Vol 59 (1) ◽  
pp. 107-112
Author(s):  
N. N. Osipov ◽  
S. A. Tikhomirov
Keyword(s):  
Projective Space ◽  
Moduli Space ◽  
Stable Rank ◽  
Irreducible Components ◽  
Rank 2 ◽  
Rank 2 Bundles

STABLE RANK-2 BUNDLES ON CALABI–YAU MANIFOLDS

2003 ◽  
Vol 14 (10) ◽  
pp. 1097-1120 ◽  
Author(s):  
WEI-PING LI ◽  
ZHENBO QIN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Double Cover ◽  
Stable Rank ◽  
Chern Classes ◽  
Canonical Divisor ◽  
Rank 2 ◽  
Stable Sheaves ◽  
Rank 2 Bundles ◽  
Calabi Yau Manifolds

In this paper, we apply the technique of chamber structures of stability polarizations to construct the full moduli space of rank-2 stable sheaves with certain Chern classes on Calabi–Yau manifolds which are anti-canonical divisor of ℙ1×ℙn or a double cover of ℙ1×ℙn. These moduli spaces are isomorphic to projective spaces. As an application, we compute the holomorphic Casson invariants defined by Donaldson and Thomas.

Restriction of Stable Bundles on an Abelian Surface. The C2 = 2 Case

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Cristian Anghel
Keyword(s):  
Moduli Space ◽  
Stable Rank ◽  
Abelian Surface ◽  
Restriction Map ◽  
Stable Bundles ◽  
Genus 2 ◽  
Rank 2 ◽  
Dimension 2 ◽  
Rank 2 Bundles

Abstract In this note we describe the restriction map from the moduli space of stable rank 2 bundles with c2 = 2 on a jacobian X of dimension 2, to the moduli space of stable rank 2 bundles on the corresponding genus 2 curve C embedded in X.

scholarly journals The moduli of a class of rank 2 vector bundles on P3

1981 ◽  
Vol 84 ◽  
pp. 9-30 ◽  
Author(s):  
G. Pete Wever
Keyword(s):  
Projective Space ◽  
Vector Bundles ◽  
Finite Union ◽  
Stable Rank ◽  
Projective Varieties ◽  
Algebraic Vector ◽  
Rank 2 ◽  
Rank 2 Vector Bundles ◽  
Rank 2 Bundles

Barth and others [1], [2], [5] have begun the study of stable algebraic vector bundles of rank 2 on projective space. Maruyama [7] has shown that stable rank 2 bundles have a variety of moduli which is the finite union of quasi-projective varieties.

scholarly journals A note on 1-cycles on the moduli space of rank-2 bundles over a curve

2019 ◽  
Vol 357 (2) ◽  
pp. 209-211
Author(s):  
Duo Li ◽  
Yinbang Lin ◽  
Xuanyu Pan
Keyword(s):  
Moduli Space ◽  
Rank 2 ◽  
Rank 2 Bundles

scholarly journals Construction of Stable Rank 2 Bundles on ℙ3 Via Symplectic Bundles

2019 ◽  
Vol 60 (2) ◽  
pp. 343-358 ◽  
Author(s):  
A. S. Tikhomirov ◽  
S. A. Tikhomirov ◽  
D. A. Vassiliev
Keyword(s):  
Stable Rank ◽  
Rank 2 ◽  
Rank 2 Bundles

A direct proof that toric rank $2$ bundles on projective space split

2020 ◽  
Vol 126 (3) ◽  
pp. 493-496
Author(s):  
David Stapleton
Keyword(s):  
Vector Bundle ◽  
Projective Space ◽  
Complete Intersection ◽  
Vector Bundles ◽  
Direct Proof ◽  
Rank 2 ◽  
Dimensional Projective Space ◽  
Rank 2 Bundles

The point of this paper is to give a short, direct proof that rank $2$ toric vector bundles on $n$-dimensional projective space split once $n$ is at least $3$. This result is originally due to Bertin and Elencwajg, and there is also related work by Kaneyama, Klyachko, and Ilten-Süss. The idea is that, after possibly twisting the vector bundle, there is a section which is a complete intersection.

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